The use of four-dimensional computed tomography (4DCT) is a common practice in radiation therapy treatment planning for thoracic regions. The information from 4DCT allows a radiation oncologist to plan accurate treatments for moving tumors, deliver radiation within predetermined certain interval in the breathing cycle, and reduce the risk of treatment-related side effects.
Methods for 4DCT include retrospective slice sorting, and prospective sinogram selection. For the retrospective slice sorting method, the projection data are continuously acquired for a time interval longer than a respiratory cycle. Multiple slices corresponding to different times are reconstructed and sorted into respiratory phase bins using various respiratory signals. For the prospective sinogram selection method, the scanner is triggered by the respiratory signal. Then, the projection data within, the same phase bin are used to reconstruct CT slices corresponding to that breathing phase.
Both methods are time consuming and considerably increase the radiation dose for the patient. For example, the radiation dose of a conventional 4DCT scan is about six times a typical helical CT scan, and 500 times a chest X-ray. Moreover, 4DCT acquisition alone cannot determine the tumor position in-situ. These facts are a major concern in the clinical application of 4DCT, motivating development of advanced 4DCT simulators.
Various methods are known for modeling lung inflation and deflation. The first category of methods discretize the soft tissues and bones into masses (nodes), and connect the nodes using springs and dampers (edges) based on a mass-spring-damper system, and CT scan values for spline-based mathematical cardiac-torso (MCAT) phantoms, augmented reality based medical visualization, respiration animation, and tumor motion modeling. A common approach applies affine transformations to control points to simulate respiratory motion. Lungs and body outline are linked to the surrounding ribs for synchronized expansion and contraction. Those simple and fast methods only provide approximate lung deformations when compared with accurate models based on continuum mechanics.
The second category of methods use hyperelastic models to describe the non-linear stress-strain behavior of the lung. To simulate lung deformation between two breathing phases (Ti,Ti+1), the lung shape at phase Ti+1 is used as the contact or constraint surface, and deform the lung at phase Ti based on the predefined mechanical properties of lung. A negative pressure load is applied on the lung surface, and finite element (FE) analysis is used to deform tissues. The lung expands according to the negative pressure, and slide against the contact surface to imitate the pleural fluid mechanism. The pressure can be estimated from the pleural pressure versus lung volume curve, which measured from a pulmonary compliance test.
In addition to lung deformation, the displacements of the rib cage and diaphragm are also very important to design a realistic 4DCT simulator. Rib cage motion can be a rigid transformation. A finite helical axis method can be used to simulate the kinematic behavior of the rib cage. The method can be developed into a chest wall model relating the ribs motion to thorax-outer surface motion for lung simulation.
A simple diaphragm model includes central tendon and peripheral muscular fiber. Then, cranio-caudal (CC) forces are applied to each node of the muscular fiber to simulate the contraction of the diaphragm. A Gauchy-Green deformation tensor can model the lung deformation. Organs inside the rib cage can be considered as a convex balloon to estimate an internal deformation field directly by interpolation of skin marker motions.